Slope, Slopes of Parallel Lines, Slopes of Perpendicular Lines.
Period 1. Elena Spaulding, Cricket Martin, Erin Sheehy.
Formulas by Elena Spaulding Slope: m= y2-y1 x2-x1
Example: Given the two points (4,3) and (1,2), find the slope. m= y2-y1 x2-x1 m= 3-2 4-1 m= 1 3
Slope- Intercept Equation: y= mx+ b
Point- Slope Equation: (y-y1) = m(x-x1) Example: The point is (-1,1) and the slope is 2. (y-y1) = m(x-x1) (y-1) = 2(x-(-1)) (y-1) = 2x + 2 y-1 = 2x + 2 Answer: y = 2x + 3
.
Cricket Martin
Formulas for slope and questions by Erin Sheehy
The slope of a line is a measure of "how steep" a line is. The slope of a line can bepositive, negative, zero, and undefined.
Now that we know the different types of slopes let's recall how to calculate the slope of a line if we know two points that the line passes through.
Slope Formula
for the most part we use the condensed formula
or
Let's look at an example
Ex.1
Don't be fooled if the coordinates are given to you as intercepts, as the next example will demonstrate.
Ex. 2 Find the slope of the line having an x intercept of 3 and a y intercept of 4 Solution: The x and y intercepts are really the points (3,0) and (0,4). Therefore we use these points in the formula
Therefore our equation becomes
and our final answer is
Now it is your turn to try.
Your Turn #1 Find the slope of the line passing through the points (4,-6) and (-3,7).
is below
Now what if you are given a linear equation and asked to find the slope. Do you remember how to do that? If you don't remember continue reading!
To find the slope of a linear equation, one must put the equation in slope intercept form.
Give it a try.
Your Turn #2 Find the slope of the linear equation
is below
Now that we know how to find the slope of a linear equation we are going to learn how to create a linear equation.
Requirements to Create a Linear Equation To create a linear equation we need two things:
1. the slope of the line
2. a point the line passes through
Once we have the above requirements we can substitute them into thepoint slope formulato find the equation.
Ex. 3 Find the equation of the line with a slope of 5 and passing through the point (-3,8). Solution: Since we already have our two requirements to create a linear equation, we simply plug in our information into the point slope formula.
Simplifying we get,
Distributing we get,
Our answer in slope intercept form is
In standard form our answer would be
Note: For our class standard form is considered to be
where A,B,C are any real number.
Sometimes we are not directly given the requirements needed to find the equation of a line. Ckeck out example 4.
Ex. 4 Find the equation of a line passing through the points (2,7) and (-3,6). Write the equation in standard form. Solution: We have one of our requirements, that being a point the line passes through. What we need to find is our slope. Using our slope formula we can get
Now that we have our slope we can use either given point to create our linear equation. Let's use the point (2,7).
Period 1.
Elena Spaulding,
Cricket Martin,
Erin Sheehy.
Formulas by Elena Spaulding
Slope: m= y2-y1
x2-x1
Example: Given the two points (4,3) and (1,2), find the slope.
m= y2-y1
x2-x1
m= 3-2
4-1
m= 1
3
Slope- Intercept Equation: y= mx+ b
Point- Slope Equation: (y-y1) = m(x-x1)
Example: The point is (-1,1) and the slope is 2.
(y-y1) = m(x-x1)
(y-1) = 2(x-(-1))
(y-1) = 2x + 2
y-1 = 2x + 2
Answer: y = 2x + 3
Cricket Martin
Formulas for slope and questions by Erin Sheehy
The slope of a line is a measure of "how steep" a line is.
The slope of a line can be positive, negative, zero, and undefined.
Now that we know the different types of slopes let's recall how to calculate the slope of a line if we know two points that the line passes through.
for the most part we use the condensed formula
or
Solution: The x and y intercepts are really the points (3,0) and (0,4). Therefore we use these points in the formula
Therefore our equation becomes
and our final answer is
Now what if you are given a linear equation and asked to find the slope. Do you remember how to do that? If you don't remember continue reading!
To find the slope of a linear equation, one must put the equation in slope intercept form.
Give it a try.
Now that we know how to find the slope of a linear equation we are going to learn how to create a linear equation.
To create a linear equation we need two things:
1. the slope of the line
2. a point the line passes through
Solution: Since we already have our two requirements to create a linear equation, we simply plug in our information into the point slope formula.
Simplifying we get,
Distributing we get,
Our answer in slope intercept form is
In standard form our answer would be
Note: For our class standard form is considered to be
where A,B,C are any real number.
Solution: We have one of our requirements, that being a point the line passes through. What we need to find is our slope. Using our slope formula we can get
Now that we have our slope we can use either given point to create our linear equation. Let's use the point (2,7).